A wireless receiver generally includes a mixer for converting the frequency of a wireless signal to within a certain frequency range and a filter for further selecting a desired frequency by filtering out unwanted frequencies.
The filter may include, but not limited to, a low pass filter (LPF), a high pass filter, a band pass filter (BPF), and a complex band pass filter. For example, FIG. 1 shows a Butterworth low pass filter (LPF) that employs passive inductors and capacitors. The bandwidth of the LPF is designed for 1 MHz. With a standard synthesis method, the resistance, capacitance and inductance in FIG. 1 can be calculated as following:Rs=1kΩ, RL=1kΩ, C1LPF=C2LPF=227.6pF, L2LPF=253.1uH.
Using transconductors and capacitors to realize a filter has gained a wide industrial acceptance. FIG. 2 illustrates a LPF implemented with transconductors and capacitors. In order to have the same bandwidth as that of the LPF in FIG. 1, the relationship between the capacitance, resistance, and inductance in FIG. 1 and transconductance and capacitance in FIG. 2 must follow the equations below:
            G      mS        =          1              R        S              ,          ⁢            G      mL        =          1              R        L              ,          ⁢            G      mG        =                  1                  1          ⁢          K          ⁢                                          ⁢          Ω                    =              1        ⁢        mS              ,          ⁢            C      ⁢                          ⁢      1        =          C      ⁢                          ⁢              1        LPF              ,          ⁢            C      ⁢                          ⁢      3        =          C      ⁢                          ⁢              3        LPF              ,          ⁢            C      ⁢                          ⁢      2        =                  G        mG        2            ⁢      L      ⁢                          ⁢              2        LPF            It should be noted that a suitable value for the transconductor GmG is required. In this example, GmG is selected to be 1 milli-siemens. Thus, the calculated values for the components in FIG. 2 are:GmS=1mS, GmL=1mS, GmG=1mS, C1=227.6pF, C2=253.1pFandC3=227.6pF.
FIG. 3 illustrates a complex BPF transformed from the LPF network of FIG. 2. The frequency responses of the LPF of FIG. 2 and the complex BPF of FIG. 3 are shown in FIG. 4. The LPF with a bandwidth of 1 MHz is transformed to a complex BPF with a center frequency of 4 MHz and a bandwidth of 2 MHz. The complex BPF receives two quadrature input signals, Vin and j*Vin, and outputs two quadrature signals, Vout and j*Vout. The complex BPF includes two LPFs 302, 304 and additional transconductors GmC1, GmC2, GmC3, 306. The center frequency of the complex BPF Fo is determined by the value of transconductors GmC1, GmC2, Gmc3 and capacitors in the two LPFs 302, 304, whereGmC1=2πF0C1 GmC2=2πF0C2   (1)GmC3=2πF0C3 Since the center frequency Fo is 4 MHz in this example, thus, the calculated values for transconductorsGmC are GmC1=5.72mS, GmC2=6.36mS, GmC3=5.72mS.
The major drawback of the above-mentioned three examples is that the pole frequencies of these filters are subject to absolute component variation. When implementing these filters in integrated circuits, variation in resistance, capacitance, transconductance can occur. For example, for a Transconductor-Capacitor (Gm-C) filter, the transconductance and capacitances can vary easily within a range of ±20%. Therefore, it is impossible to obtain a desired filter frequency response as designed. Either the transconductors or the capacitors need to be adjusted in order to get the desired frequency response. Such adjustment may be referred to as filter tuning or filter trimming.
FIG. 5 illustrates a traditional method for filter tuning employing a separate tuning device. Device 500 includes a main filter 502 and a tuning device 504. The tuning device 504 includes a voltage control oscillator (VCO) 506, a phase detector 508, and a loop filter 510. The voltage control oscillator (VCO) 506 utilizes transconductors and capacitors that are duplicates of the transconductors and capacitors in the main filter to generate a frequency Fvco. It should be noted that it is also possible to use a voltage controlled low pass filter (VCLPF) instead of a VCO 506 in the tuning device 504. The phase detector 508 receives Fvco and a reference frequency Fref, and detects the phase difference between Fvco and Fref. A detected difference is provided to the loop filter 510 where the loop filter 510 is capable of adjusting the value of the components (i.e. transconductors or capacitors) in the main filter 502 to nominal design values. Therefore, the frequency of the main filter can be kept at a stable and accurate value.
However, there are several disadvantages with this tuning approach. Firstly, the continuous tuning of VCO 506 will generate noise that affects the operation of the filter. Secondly, the VOC 506 consumes additional power and occupies additional physical area. Thirdly, the pole frequency of VCO 506 could be very different from that of the filter under certain circumstance which may result in poor tuning accuracy.
Thus, it is to an improved filter tuning method that is able to provide an accurate tuning without requiring additional power and area and without introducing additional noise sources that present invention is directed to.